Trial of Ado-Trastuzumab Emtansine for Patients With HER2 Amplified or Mutant Cancers

Inclusion Criteria: * Adults who are ≥18 years old. * Pathologically confirmed advanced solid tumor cancers * For Cohort 1, documented activating HER2 mutation in lung cancer by CLIA laboratory, specifically exon 20 insYVMA (Y772\_A775dup), insGSP (G778\_P780dup), insTGT (G776delinsVC), single base pair substitutions L755A, L755S, V777L, V659E, S310F, or another HER2 mutation approved by the Principal Investigator * For Cohorts 2, 3, 4, 5, 6 documented HER2 amplification identified through next generation sequencing by MSK-IMPACT or at another Clinical Laboratory Improvement Amendments (CLIA) laboratory, or documented HER2 amplification by in-situ hybridization (ISH) with HER2/CEP17 ratio ≥2.0 at a CLIA laboratory. Patients with HER2 amplification identified by another method or criteria must be approved by the Principal Investigator and may enroll in the "Other" Cohort 4. * Measurable or evaluable indicator lesion(s) as defined by RECIST v1.1. Patients without RECIST measurable disease will be eligible for enrollment to "Other" cohort provided their disease can be evaluated using another accepted response criteria (e.g. Gynecologic Cancer InterGroup (GCIG) CA125 Response Criteria, modified PET Response Criteria in Solid Tumors (PERCIST)). Patients with salivary gland cancers (Cohort 5) may be eligible on the basis of evaluable disease on modified PET. * Karnofsky Performance Status 70% or above. * Left ventricular ejection fraction (LVEF) ≥50% measured by echocardiogram (EC…